Exam 5: Inverse, Exponential, and Logarithmic Functions

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$ . Find $f ( 3 )$

Find the value. Give an approximation to four decimal places. - $\log 144$

Determine whether the statement is true or false. -Any polynomial function of odd degree is a one-to-one function.

Solve the equation. Round to the nearest thousandth. - $3 ^ { ( x + 6 ) } = 4 ^ { x }$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = - 8 x + 1$

Solve the problem. -Suppose that the salinity $S$ of ocean water at a given depth $d$ is modeled by the equation $\mathrm { S } ( \mathrm { d } ) = 28.4 + 1.3 \log ( \mathrm { d } + 1 )$ , where $\mathrm { S }$ is measured in grams salt per kilogram water and $\mathrm { d }$ is measured in meters. What is the salinity when the depth is $17 \mathrm {~m}$ ? Round your answer to the nearest hundredth.

Use the alphabet coding method (A =1, B = 2, C = 3, ... Z = 26) to -Encode the message BEWARE OF DOG using the one-to-one function defined by $f ( x ) = x ^ { 3 } - 1$ Give the inverse function that the decoder would need when the message is received.

Write the word or phrase that best completes each statement or answers the question. - $\text { With the function } f ( x ) = \log _ { a } x \text {, why can't } x \text { be less than } 0 \text { ? }$

Choose the one alternative that best completes the statement or answers the question. -Suppose the number of Quickie hamburgers (in millions) served yearly can be modeled by $f ( x ) = 39.6 e ^ { 0.14 x }$ . Approximate how many years it takes for the number of hamburgers served to reach 152 million. Round to the nearest year.

Solve the equation. - $4 ^ { ( 7 + 3 x ) } = \frac { 1 } { 16 }$

Choose the one alternative that best completes the statement or answers the question. -In year 0, the number of female athletes participating in Summer Olympic-Type Games was 550. In year 11, about 3600 participated in the Summer Olympics in Atlanta. Assuming that and $P ( 0 ) = 500$ that the exponential model applies, find the value of k rounded to the hundredths place, and write The function.

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected. -

Solve for the indicated variable. - $P = 30,000 \cdot e ^ { t / 3 } \text {, for } t$

Find the value. Give an approximation to four decimal places. - $\log 2.67$

Solve the problem. -Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by $\ln ( 1 - \mathrm { P } ) = - 0.0025 - 0.0046 \mathrm { x }$ where x represents the dollars of tax per ton of Carbon emitted and P represents the percent reduction in emissions of carbon. (P is in decimal Form.) Determine P when x = 62. Round to three decimal places.

Find the value. Give an approximation to four decimal places. - $\ln ( 454 \times 28 )$

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 2 } - 5 ; x \geq 0$

Match the function with its graph. - $f ( x ) = \log _ { 5 } ( - x )$

Decide whether the given functions are inverses. - x f(x) 2 36 3 49 4 64 5 81 6 100 () 36 2 49 3 64 4 81 5 100 6

Write an equivalent expression in exponential form. - $\log _ { x } 16 = 2$